Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 6x - 7$ and $ JT = 4x + 5$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {6x - 7} = {4x + 5}$ Solve for $x$ $ 2x = 12$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 6({6}) - 7$ $ JT = 4({6}) + 5$ $ CJ = 36 - 7$ $ JT = 24 + 5$ $ CJ = 29$ $ JT = 29$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {29} + {29}$ $ CT = 58$